### A Dipole in front of a flat Metallic surface

Tags: Image Charges / Dipole / Green's Function

The potential of a dipole in front of a flat metallic surface is calculated. A Taylor expansion is used to understand the resulting electric field.

The fundamental solution to the **Poisson equation** with respect to a point-like excitation is known. Such a solution is called **Green's function** - in three dimensions, we have the famous \(1/r\)-dependency. However, if one knows the Green's function for a differential operator (here Laplace \(\Delta\)) any problem can be solved with respect to the given **boundary conditions**. In this section we will learn different techniques to solve such boundary value problems, for example the method of mirror charges or direct integrations.

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in
Electrodynamics /
Electrostatics /
Boundary Value Problems

Tags: Image Charges / Dipole / Green's Function

Tags: Image Charges / Dipole / Green's Function

The potential of a dipole in front of a flat metallic surface is calculated. A Taylor expansion is used to understand the resulting electric field.

A derivation of the boundary integral equation in electrostatics. The relation to the Boundary Element Method is explained.

The electrostatic field of a point charge close to a grounded metallic sphere is derived.

Published
in
Electrodynamics /
Electrostatics /
Boundary Value Problems

Tags: Image Charges / Dipole

Tags: Image Charges / Dipole

A point charge in front of two grounded metallic half-planes, problem and solution.